3. Models
3.1 Linear Model
This chapter will be focused on the continous variable
nwspol. The question in the survey was: On a typical day,
about how much time do you spend watching, reading or listening to news
about politics and current affairs?
The older the person, the more they watch the news. The same
hypothesis can be made for education, satisfaction with democracy,
confidence in own ability to participate and interest in
politics.
Graphical analysis
This plot shows in the upper half news consumption variable
with outliers. As can be seen, there are a lot of outliers. In the
second half of the plot, there are no outliers and there can bee seen an
increase in news consumption (interest in politics and confidence in
ability) with every step.
Interpretation:
Age: The relationship between age and news
consumption is not at every point positively linear. It starts to grow
from the age smallest age (15y) to approximitely 25 and then it
stagnates till around the age 50 and then the news consumption grows
with every year. This can be explained that news consumption is not that
important during the time between the ages 25 to 50 because of family
matters such as raising children or focusing on career. Afterwards or
beforehand the obligations are lighter.
Education in years: there is a small positive
slope. This also confirms the hypothesis that with each additional
educational year ones ability in understanding of current affairs is
heightend and therefore one is more interested in news and consumes it
more frequently. One of the reasons is the ability to understand it.
Fitting Model
##
## Call:
## lm(formula = nwspol.na ~ age.na, data = ess9_linear)
##
## Residuals:
## Min 1Q Median 3Q Max
## -92.23 -34.89 -15.36 13.66 1119.49
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15.09729 4.62268 3.266 0.00111 **
## age.na 0.97636 0.08713 11.206 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 79.21 on 2294 degrees of freedom
## Multiple R-squared: 0.0519, Adjusted R-squared: 0.05149
## F-statistic: 125.6 on 1 and 2294 DF, p-value: < 0.00000000000000022

Interpretation: age is a highly significant
predictor. It is a positive relationship to the news consumption in
minute. The p-Value is <0.05. For every additional year a person
nearly 1 minute (0.97) is added to the news consumption. This does not
dismis the hypothesis that with every additional year, a person is
following the news. There is the common knowledge that the older
population is more likely to vote and that young people are more focused
on other life topics.
Adding additional predictors
##
## Call:
## lm(formula = nwspol.na ~ age.na + ability.fac, data = ess9_linear)
##
## Residuals:
## Min 1Q Median 3Q Max
## -94.39 -34.31 -14.34 12.98 1118.68
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.78717 4.82835 3.477 0.000517 ***
## age.na 1.00102 0.08729 11.468 < 0.0000000000000002 ***
## ability.fac.L 23.91718 5.60431 4.268 0.0000206 ***
## ability.fac.Q 6.14664 4.96852 1.237 0.216170
## ability.fac.C -0.16275 4.08717 -0.040 0.968240
## ability.fac^4 1.05014 3.23978 0.324 0.745862
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 78.87 on 2290 degrees of freedom
## Multiple R-squared: 0.0616, Adjusted R-squared: 0.05956
## F-statistic: 30.07 on 5 and 2290 DF, p-value: < 0.00000000000000022
{drop1(lm_news.1, test = "F")}
Interpretation: the Variable Confidence
in ability might have an influence on the dependent variable as it
is significant in the single term deletions.
##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lm(formula = nwspol.na ~ age.na + ability.fac, data = ess9_linear)
##
## Linear Hypotheses:
## Estimate Std. Error t value Pr(>|t|)
## a little - not at all == 0 1.853 6.232 0.297 0.99818
## quite - not at all == 0 9.132 6.186 1.476 0.56370
## very - not at all == 0 17.185 6.786 2.533 0.07846 .
## completely - not at all == 0 30.150 8.512 3.542 0.00346 **
## quite - a little == 0 7.279 4.029 1.806 0.35566
## very - a little == 0 15.332 4.876 3.144 0.01348 *
## completely - a little == 0 28.297 7.103 3.984 < 0.001 ***
## very - quite == 0 8.054 4.812 1.674 0.43565
## completely - quite == 0 21.019 7.060 2.977 0.02268 *
## completely - very == 0 12.965 7.576 1.711 0.41230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)

Interpretation: When comparing the different
self assumed levels of confidence in ones ability it is
observable that the polar opposites completely and not at
all have significant difference (p<.05) and the next biggest
difference completely and a little are also
significant. The others have a lower level of significants or none at
all.
##
## Call:
## lm(formula = nwspol.na ~ eduyrs.na + age.na + gndr.fac + stfdem.na +
## ability.fac + interest.fac, data = ess9_linear)
##
## Residuals:
## Min 1Q Median 3Q Max
## -100.69 -31.90 -12.93 13.30 1127.04
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 49.64547 10.03733 4.946 0.0000008123487802 ***
## eduyrs.na -0.96445 0.49499 -1.948 0.05149 .
## age.na 0.71236 0.09329 7.636 0.0000000000000328 ***
## gndr.fac2 -2.69782 3.31452 -0.814 0.41576
## stfdem.na -1.03706 0.70387 -1.473 0.14079
## ability.fac.L 10.55681 6.05077 1.745 0.08117 .
## ability.fac.Q 7.68736 5.00224 1.537 0.12448
## ability.fac.C 1.17460 4.04289 0.291 0.77143
## ability.fac^4 0.98067 3.20308 0.306 0.75951
## interest.fac.L 29.65914 6.75701 4.389 0.0000118846240809 ***
## interest.fac.Q 13.83210 5.04290 2.743 0.00614 **
## interest.fac.C -2.64438 3.33380 -0.793 0.42774
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 77.76 on 2284 degrees of freedom
## Multiple R-squared: 0.09036, Adjusted R-squared: 0.08598
## F-statistic: 20.62 on 11 and 2284 DF, p-value: < 0.00000000000000022
Interpretation: Age and two expressions of
the predictor variable interest in politics show signifcant
values. Interest is here only significant in terms of the
reference level. This linear regression also shows a higher adjusted R2
(0.085) then the one with the two predictors. However, it is still a
small value and the model explains roughly 8% of the variations of the
data.
## 2.5 % 97.5 %
## (Intercept) 29.9622382 69.328698532
## eduyrs.na -1.9351294 0.006238564
## age.na 0.5294131 0.895310385
## gndr.fac2 -9.1975974 3.801961940
## stfdem.na -2.4173456 0.343229267
## ability.fac.L -1.3087655 22.422383039
## ability.fac.Q -2.1220445 17.496772989
## ability.fac.C -6.7535159 9.102714457
## ability.fac^4 -5.3005776 7.261926573
## interest.fac.L 16.4086202 42.909662132
## interest.fac.Q 3.9429471 23.721250676
## interest.fac.C -9.1819647 3.893205185

Interaction: Age * ability
The background to this interaction: With every additional year on
this earth one grows in his confidence in the own ability to participate
in the political landscape. So therefore, the level of confidence in
ones ability is dependent/varies on the age.
##
## Call:
## lm(formula = nwspol.na ~ eduyrs.na + age.na * ability.fac + gndr.fac +
## stfdem.na + interest.fac, data = ess9_linear)
##
## Residuals:
## Min 1Q Median 3Q Max
## -117.14 -32.18 -13.15 13.67 1125.16
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45.0916 10.5389 4.279 0.00001958665556 ***
## eduyrs.na -0.9450 0.4967 -1.903 0.0572 .
## age.na 0.7880 0.1112 7.085 0.00000000000184 ***
## ability.fac.L -18.9613 16.1182 -1.176 0.2396
## ability.fac.Q -9.8818 14.1288 -0.699 0.4844
## ability.fac.C -21.9343 11.4716 -1.912 0.0560 .
## ability.fac^4 -13.6327 9.0569 -1.505 0.1324
## gndr.fac2 -2.4310 3.3153 -0.733 0.4635
## stfdem.na -1.0179 0.7037 -1.447 0.1482
## interest.fac.L 30.7487 6.7908 4.528 0.00000626223350 ***
## interest.fac.Q 13.1529 5.1038 2.577 0.0100 *
## interest.fac.C -2.4369 3.3424 -0.729 0.4660
## age.na:ability.fac.L 0.5682 0.2901 1.959 0.0503 .
## age.na:ability.fac.Q 0.3716 0.2571 1.445 0.1485
## age.na:ability.fac.C 0.4680 0.2178 2.149 0.0317 *
## age.na:ability.fac^4 0.3051 0.1740 1.753 0.0797 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 77.69 on 2280 degrees of freedom
## Multiple R-squared: 0.09361, Adjusted R-squared: 0.08765
## F-statistic: 15.7 on 15 and 2280 DF, p-value: < 0.00000000000000022
## Single term deletions
##
## Model:
## nwspol.na ~ eduyrs.na + age.na * ability.fac + gndr.fac + stfdem.na +
## interest.fac
## Df Sum of Sq RSS AIC
## <none> 13759932 20003
## eduyrs.na 1 21851 13781784 20005
## gndr.fac 1 3245 13763177 20002
## stfdem.na 1 12628 13772560 20004
## interest.fac 3 408076 14168008 20064
## age.na:ability.fac 4 49448 13809380 20004
Interpretation: Nothing is significant, not
even the interaction. The hypothesis on the interaction has to be
dismissed. Also the adjusted R2 has not increased (a lot), therefore,
this interaction is not useful.
## 2.5 % 97.5 %
## (Intercept) 24.4246611513 65.75845544
## eduyrs.na -1.9189916573 0.02889455
## age.na 0.5698937223 1.00609375
## ability.fac.L -50.5692499912 12.64663750
## ability.fac.Q -37.5885428572 17.82493581
## ability.fac.C -44.4301641545 0.56152951
## ability.fac^4 -31.3933160345 4.12783323
## gndr.fac2 -8.9322647665 4.07025536
## stfdem.na -2.3979510424 0.36206988
## interest.fac.L 17.4318131927 44.06559034
## interest.fac.Q 3.1442173901 23.16150527
## interest.fac.C -8.9914422606 4.11764654
## age.na:ability.fac.L -0.0006799644 1.13710009
## age.na:ability.fac.Q -0.1325726928 0.87579856
## age.na:ability.fac.C 0.0409404664 0.89515543
## age.na:ability.fac^4 -0.0361108509 0.64632065

The interaction is not significant. Therefore, let’s focus on the
interest in politics variable
##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lm(formula = nwspol.na ~ eduyrs.na + age.na * ability.fac + gndr.fac +
## stfdem.na + interest.fac, data = ess9_linear)
##
## Linear Hypotheses:
## Estimate Std. Error t value Pr(>|t|)
## hardly - none at all == 0 -1.581 9.232 -0.171 0.998059
## quite - none at all == 0 15.439 9.390 1.644 0.333749
## very - none at all == 0 40.164 9.852 4.077 0.000234 ***
## quite - hardly == 0 17.021 4.184 4.068 0.000233 ***
## very - hardly == 0 41.745 5.139 8.123 < 0.0001 ***
## very - quite == 0 24.724 4.353 5.679 < 0.0001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)


Interpretation: the different stages of
political interest indicate a different usage of news according to the
age. While the lowest level of political interest shows a positive
relationship between news consumption and age, it has the the second
smallest slope. The most interest category expression has the biggest
slope over the lifetime.
Fitted Values and Residuals
Fitted Values
There are 185 unique fitted values from the first linear
regression.

Residuals

Predicted values
one predictor variable

3.2 GLM Poisson
The goal of this chapter is to apply a generalized linear model of
the poisson type on the ESS9 data set. The poisson model is applied to
count data, in this case the information of how many minutes the
participants spend per day for consuming media, such as newspaper, TV
new shows or online resources.
In this chapter the model is used to simulate the data, based on the
survey data. Getting a simulation of the minutes according to a selected
subset of variables from the study.
First the data is cleaned and prepared for using it. A subset of the
data is used, containing social and demographic variables which should
help to model the news consumption of a person. These parameters are
used:
Depended variable:
- How much politics are you watching (“nwspol”)
Independent variables:
- Interest in politics (“polintr)
- Trust into the current parlament (“trstprl”)
- Highest level of education (“eisced”)
- Years of education (“eduyrs”)
- Satisfaction with the general economical situation (“stfeco”)
- Satisfaction with the current government (“stfgov”)
- Satisfaction with the democratic system (“stfdem”)
- Gender (“gndr”)
- Age (“agea”)
- Level of religiouse believes (“rlgdgr”)
- Time spent online in 5 categorical values(“netusoft”)
- Possibility for political participation (“psppsgva”)
- Yearly gross income (combination of two factors into a new one -
“yrpy”)
3.2.1 Data preparation
The data have to be prepared and transformed. For poisson count data
are needed for the predictive variable. The time in minutes is modeled
therefore.
## [1] 572
## [1] 708
## [1] 1752
## [1] 47
Subset data for this task, to the defined 14 variables in total. The
rows with NA are dropped, as the data set is large enough for dropping
theses values.
## tibble [17,029 × 14] (S3: tbl_df/tbl/data.frame)
## $ nwspol : num [1:17029] 60 45 60 120 15 60 30 30 10 10 ...
## $ polintr : Factor w/ 4 levels "1","2","3","4": 4 3 4 2 4 1 2 3 2 2 ...
## $ trstprl : Factor w/ 11 levels "0","1","2","3",..: 7 1 1 7 5 4 4 8 8 6 ...
## $ eisced : Factor w/ 8 levels "1","2","3","4",..: 2 3 3 3 3 4 3 6 2 7 ...
## $ eduyrs : num [1:17029] 12 11 12 12 13 21 18 17 9 17 ...
## $ stfeco : Factor w/ 11 levels "0","1","2","3",..: 6 7 2 11 10 8 7 8 7 9 ...
## $ stfgov : Factor w/ 11 levels "0","1","2","3",..: 7 9 4 11 9 3 8 3 8 7 ...
## $ stfdem : Factor w/ 11 levels "0","1","2","3",..: 7 7 4 11 8 4 11 7 9 8 ...
## $ gndr : Factor w/ 2 levels "1","2": 2 1 1 1 2 1 1 1 1 1 ...
## $ agea : num [1:17029] 40 63 56 48 41 27 49 42 50 35 ...
## $ rlgdgr : Factor w/ 11 levels "0","1","2","3",..: 5 2 9 1 4 4 3 1 4 3 ...
## $ netusoft: Factor w/ 5 levels "1","2","3","4",..: 4 5 1 1 4 5 5 5 5 5 ...
## $ psppsgva: Factor w/ 5 levels "1","2","3","4",..: 2 2 2 5 1 3 1 1 2 3 ...
## $ yrpy : num [1:17029] 31200 30600 18000 31200 37200 18000 20400 17400 45600 70000 ...
The plot shows the media consumption for male and female to gain a
quick overview. Males have a higher mean and the variance of values
between the first and third quantile is larger as well in
comparison.

The second plot indicates the frequency of internet usage and the
media consumption. The mean of the two lower frequencies (“never” and
“only occasionally”) have higher values for media consumption.

3.2.2 Fitting the poisson model
Using the parameter specified above to model the consumption. Using
the subset variables of the survey.
##
## Call:
## glm(formula = nwspol ~ polintr + eisced + trstprl + eduyrs +
## netusoft + stfeco + stfgov + stfdem + gndr + agea + rlgdgr +
## yrpy, family = "poisson", data = ess9_poisson)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -17.160 -6.476 -3.322 0.474 74.725
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.9551478455834 0.0105343674796 470.379 < 0.0000000000000002 ***
## polintr2 -0.3492665558265 0.0026678349780 -130.918 < 0.0000000000000002 ***
## polintr3 -0.5376726514740 0.0028816344085 -186.586 < 0.0000000000000002 ***
## polintr4 -0.6563093286586 0.0037354537637 -175.697 < 0.0000000000000002 ***
## eisced2 -0.1458105762706 0.0064736859414 -22.524 < 0.0000000000000002 ***
## eisced3 -0.2098897454780 0.0063900096516 -32.847 < 0.0000000000000002 ***
## eisced4 -0.0801180098272 0.0062959701053 -12.725 < 0.0000000000000002 ***
## eisced5 -0.1793751705951 0.0066035938535 -27.163 < 0.0000000000000002 ***
## eisced6 -0.0136582683597 0.0068047744981 -2.007 0.0447 *
## eisced7 -0.0747622892396 0.0070310740541 -10.633 < 0.0000000000000002 ***
## eisced55 0.1991819464428 0.0184339911655 10.805 < 0.0000000000000002 ***
## trstprl1 0.0438116718767 0.0056421385757 7.765 0.000000000000008159 ***
## trstprl2 0.0878787242680 0.0050348881462 17.454 < 0.0000000000000002 ***
## trstprl3 0.0575992821977 0.0049226015149 11.701 < 0.0000000000000002 ***
## trstprl4 0.1649699717288 0.0049617090096 33.249 < 0.0000000000000002 ***
## trstprl5 0.1785393616823 0.0046962221481 38.018 < 0.0000000000000002 ***
## trstprl6 0.0926411783091 0.0050274726710 18.427 < 0.0000000000000002 ***
## trstprl7 0.1654323040088 0.0050166399191 32.977 < 0.0000000000000002 ***
## trstprl8 0.2017014330997 0.0053305193535 37.839 < 0.0000000000000002 ***
## trstprl9 0.1425488919881 0.0068020761893 20.957 < 0.0000000000000002 ***
## trstprl10 0.1034979576788 0.0080156227526 12.912 < 0.0000000000000002 ***
## eduyrs -0.0047838263191 0.0003248431772 -14.727 < 0.0000000000000002 ***
## netusoft2 -0.1307787280215 0.0062823662011 -20.817 < 0.0000000000000002 ***
## netusoft3 -0.1124713541777 0.0061051654140 -18.422 < 0.0000000000000002 ***
## netusoft4 -0.1650624943097 0.0053911538839 -30.617 < 0.0000000000000002 ***
## netusoft5 -0.2565499520473 0.0047119730917 -54.446 < 0.0000000000000002 ***
## stfeco1 0.2042630443847 0.0078684572864 25.960 < 0.0000000000000002 ***
## stfeco2 0.1454844795976 0.0065882376682 22.082 < 0.0000000000000002 ***
## stfeco3 0.1097594146381 0.0063537352177 17.275 < 0.0000000000000002 ***
## stfeco4 0.1173993792901 0.0063956760982 18.356 < 0.0000000000000002 ***
## stfeco5 0.1060677186837 0.0062503682707 16.970 < 0.0000000000000002 ***
## stfeco6 0.0454950862456 0.0063907869403 7.119 0.000000000001088272 ***
## stfeco7 -0.0695855130540 0.0063960463742 -10.879 < 0.0000000000000002 ***
## stfeco8 -0.0844850487183 0.0065231751269 -12.952 < 0.0000000000000002 ***
## stfeco9 -0.1059951308680 0.0073197601880 -14.481 < 0.0000000000000002 ***
## stfeco10 -0.2077250234061 0.0087105452425 -23.848 < 0.0000000000000002 ***
## stfgov1 -0.0371282966740 0.0053909882570 -6.887 0.000000000005693961 ***
## stfgov2 -0.1628748230687 0.0050296948069 -32.383 < 0.0000000000000002 ***
## stfgov3 -0.1492579265587 0.0049582011543 -30.103 < 0.0000000000000002 ***
## stfgov4 -0.0842706452037 0.0050657063724 -16.636 < 0.0000000000000002 ***
## stfgov5 -0.0532296925917 0.0049390418045 -10.777 < 0.0000000000000002 ***
## stfgov6 -0.1646096319626 0.0052200210811 -31.534 < 0.0000000000000002 ***
## stfgov7 -0.0601493306535 0.0052887394475 -11.373 < 0.0000000000000002 ***
## stfgov8 -0.1257885537272 0.0059854927793 -21.016 < 0.0000000000000002 ***
## stfgov9 0.1018727906473 0.0080519498858 12.652 < 0.0000000000000002 ***
## stfgov10 0.0782407518655 0.0098315985238 7.958 0.000000000000001747 ***
## stfdem1 -0.0563098592349 0.0069113969117 -8.147 0.000000000000000372 ***
## stfdem2 -0.0025138003015 0.0061045169098 -0.412 0.6805
## stfdem3 -0.1749548063588 0.0060699082915 -28.823 < 0.0000000000000002 ***
## stfdem4 -0.0834553121230 0.0061336706557 -13.606 < 0.0000000000000002 ***
## stfdem5 -0.0745510981878 0.0059070855389 -12.621 < 0.0000000000000002 ***
## stfdem6 -0.1142834927352 0.0061219691225 -18.668 < 0.0000000000000002 ***
## stfdem7 -0.0757921344766 0.0060426970153 -12.543 < 0.0000000000000002 ***
## stfdem8 -0.1281854636406 0.0062024480020 -20.667 < 0.0000000000000002 ***
## stfdem9 -0.1819244111818 0.0069479462167 -26.184 < 0.0000000000000002 ***
## stfdem10 -0.1081689324763 0.0079802880965 -13.555 < 0.0000000000000002 ***
## gndr2 -0.0955221839468 0.0018928147422 -50.466 < 0.0000000000000002 ***
## agea 0.0039442838404 0.0000752630756 52.407 < 0.0000000000000002 ***
## rlgdgr1 0.0524594264550 0.0039129662333 13.407 < 0.0000000000000002 ***
## rlgdgr2 0.0229590182679 0.0037164081451 6.178 0.000000000650240197 ***
## rlgdgr3 0.1252369296839 0.0035904157083 34.881 < 0.0000000000000002 ***
## rlgdgr4 0.0911051329206 0.0040471525705 22.511 < 0.0000000000000002 ***
## rlgdgr5 0.0008947887099 0.0032698289371 0.274 0.7844
## rlgdgr6 0.0599344542248 0.0035893248803 16.698 < 0.0000000000000002 ***
## rlgdgr7 -0.0077316837152 0.0035782505209 -2.161 0.0307 *
## rlgdgr8 0.0079295142834 0.0038527509859 2.058 0.0396 *
## rlgdgr9 -0.0750978361239 0.0059677036213 -12.584 < 0.0000000000000002 ***
## rlgdgr10 0.1758154007801 0.0047371153192 37.114 < 0.0000000000000002 ***
## yrpy -0.0000000085380 0.0000000005367 -15.907 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1622523 on 17028 degrees of freedom
## Residual deviance: 1532064 on 16960 degrees of freedom
## AIC: 1622455
##
## Number of Fisher Scoring iterations: 6
The summary shows the residual deviance as 1532064 on 16960 degrees
of freedom. This indicates an overdispersion as the difference between
these two numbers is large. For an non-overdispersed result the should
be similar or the same.
To compare the model for the two gender, the coefficient can be
calculated.
## (Intercept) polintr2 polintr3 polintr4
## 4.955147845583398 -0.349266555826538 -0.537672651474009 -0.656309328658579
## eisced2 eisced3 eisced4 eisced5
## -0.145810576270611 -0.209889745477968 -0.080118009827152 -0.179375170595105
## eisced6 eisced7 eisced55 trstprl1
## -0.013658268359742 -0.074762289239633 0.199181946442816 0.043811671876679
## trstprl2 trstprl3 trstprl4 trstprl5
## 0.087878724267998 0.057599282197725 0.164969971728847 0.178539361682290
## trstprl6 trstprl7 trstprl8 trstprl9
## 0.092641178309068 0.165432304008800 0.201701433099665 0.142548891988131
## trstprl10 eduyrs netusoft2 netusoft3
## 0.103497957678787 -0.004783826319139 -0.130778728021462 -0.112471354177693
## netusoft4 netusoft5 stfeco1 stfeco2
## -0.165062494309659 -0.256549952047336 0.204263044384658 0.145484479597629
## stfeco3 stfeco4 stfeco5 stfeco6
## 0.109759414638132 0.117399379290054 0.106067718683748 0.045495086245550
## stfeco7 stfeco8 stfeco9 stfeco10
## -0.069585513054008 -0.084485048718322 -0.105995130868024 -0.207725023406075
## stfgov1 stfgov2 stfgov3 stfgov4
## -0.037128296673999 -0.162874823068651 -0.149257926558705 -0.084270645203717
## stfgov5 stfgov6 stfgov7 stfgov8
## -0.053229692591687 -0.164609631962625 -0.060149330653520 -0.125788553727176
## stfgov9 stfgov10 stfdem1 stfdem2
## 0.101872790647289 0.078240751865529 -0.056309859234943 -0.002513800301504
## stfdem3 stfdem4 stfdem5 stfdem6
## -0.174954806358804 -0.083455312122970 -0.074551098187797 -0.114283492735243
## stfdem7 stfdem8 stfdem9 stfdem10
## -0.075792134476610 -0.128185463640629 -0.181924411181762 -0.108168932476321
## gndr2 agea rlgdgr1 rlgdgr2
## -0.095522183946788 0.003944283840447 0.052459426455015 0.022959018267916
## rlgdgr3 rlgdgr4 rlgdgr5 rlgdgr6
## 0.125236929683865 0.091105132920631 0.000894788709914 0.059934454224848
## rlgdgr7 rlgdgr8 rlgdgr9 rlgdgr10
## -0.007731683715226 0.007929514283363 -0.075097836123885 0.175815400780054
## yrpy
## -0.000000008538016
## gndr2
## 0.9089
Female do consume approx. 10% less media compared to male
participants.
3.2.3 Simulation
Now we simulate with our model the average media consumption for
Females and Males.
## [1] 17029
## sim_1
## 1 48
## 2 47
## 3 53
## 4 81
## 5 44
## 6 79

The simulated data look similar as the real data based of the survey.
The variance is smaller for the simulated one. The higher mean and the
higher variance for the male group is indicated in the real data as well
as in the simulated data.
3.2.4 GLM Quasi-Poisson
In chapter 3.2.2 the data showed a overdispersion for the poisson
model. This isn’t unusual and can be handled by the quasipoisson model
type. The value for the dispersion parameter of 206.3327 indicates a
much faster increase of variance than linearly.
##
## Call:
## glm(formula = nwspol ~ polintr + eisced + trstprl + eduyrs +
## netusoft + stfeco + stfgov + stfdem + gndr + agea + rlgdgr +
## yrpy, family = "quasipoisson", data = ess9_poisson)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -17.160 -6.476 -3.322 0.474 74.725
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.955147845583 0.151318671203 32.746 < 0.0000000000000002 ***
## polintr2 -0.349266555827 0.038321545611 -9.114 < 0.0000000000000002 ***
## polintr3 -0.537672651474 0.041392621858 -12.990 < 0.0000000000000002 ***
## polintr4 -0.656309328659 0.053657127583 -12.232 < 0.0000000000000002 ***
## eisced2 -0.145810576271 0.092989878732 -1.568 0.116894
## eisced3 -0.209889745478 0.091787928543 -2.287 0.022227 *
## eisced4 -0.080118009827 0.090437117569 -0.886 0.375685
## eisced5 -0.179375170595 0.094855913182 -1.891 0.058638 .
## eisced6 -0.013658268360 0.097745729573 -0.140 0.888873
## eisced7 -0.074762289240 0.100996361201 -0.740 0.459160
## eisced55 0.199181946443 0.264791128042 0.752 0.451927
## trstprl1 0.043811671877 0.081045294240 0.541 0.588802
## trstprl2 0.087878724268 0.072322575173 1.215 0.224347
## trstprl3 0.057599282198 0.070709657845 0.815 0.415319
## trstprl4 0.164969971729 0.071271409098 2.315 0.020643 *
## trstprl5 0.178539361682 0.067457879792 2.647 0.008136 **
## trstprl6 0.092641178309 0.072216057163 1.283 0.199568
## trstprl7 0.165432304009 0.072060452413 2.296 0.021703 *
## trstprl8 0.201701433100 0.076569106494 2.634 0.008440 **
## trstprl9 0.142548891988 0.097706970293 1.459 0.144599
## trstprl10 0.103497957679 0.115138700652 0.899 0.368720
## eduyrs -0.004783826319 0.004666140422 -1.025 0.305273
## netusoft2 -0.130778728021 0.090241707193 -1.449 0.147299
## netusoft3 -0.112471354178 0.087696344343 -1.283 0.199682
## netusoft4 -0.165062494310 0.077440078253 -2.131 0.033063 *
## netusoft5 -0.256549952047 0.067684130856 -3.790 0.000151 ***
## stfeco1 0.204263044385 0.113024773751 1.807 0.070742 .
## stfeco2 0.145484479598 0.094635332540 1.537 0.124234
## stfeco3 0.109759414638 0.091266872185 1.203 0.229140
## stfeco4 0.117399379290 0.091869323004 1.278 0.201304
## stfeco5 0.106067718684 0.089782079758 1.181 0.237464
## stfeco6 0.045495086246 0.091799093740 0.496 0.620187
## stfeco7 -0.069585513054 0.091874641754 -0.757 0.448823
## stfeco8 -0.084485048718 0.093700755564 -0.902 0.367257
## stfeco9 -0.105995130868 0.105143131500 -1.008 0.313419
## stfeco10 -0.207725023406 0.125120766301 -1.660 0.096893 .
## stfgov1 -0.037128296674 0.077437699141 -0.479 0.631617
## stfgov2 -0.162874823069 0.072247976560 -2.254 0.024185 *
## stfgov3 -0.149257926559 0.071221021260 -2.096 0.036124 *
## stfgov4 -0.084270645204 0.072765256999 -1.158 0.246833
## stfgov5 -0.053229692592 0.070945810873 -0.750 0.453093
## stfgov6 -0.164609631963 0.074981877665 -2.195 0.028154 *
## stfgov7 -0.060149330654 0.075968967960 -0.792 0.428511
## stfgov8 -0.125788553727 0.085977332347 -1.463 0.143474
## stfgov9 0.101872790647 0.115660513996 0.881 0.378443
## stfgov10 0.078240751866 0.141223896670 0.554 0.579573
## stfdem1 -0.056309859235 0.099277284456 -0.567 0.570587
## stfdem2 -0.002513800302 0.087687029042 -0.029 0.977130
## stfdem3 -0.174954806359 0.087189900939 -2.007 0.044809 *
## stfdem4 -0.083455312123 0.088105801797 -0.947 0.343542
## stfdem5 -0.074551098188 0.084851068293 -0.879 0.379625
## stfdem6 -0.114283492735 0.087937717623 -1.300 0.193757
## stfdem7 -0.075792134477 0.086799030374 -0.873 0.382571
## stfdem8 -0.128185463641 0.089093739295 -1.439 0.150234
## stfdem9 -0.181924411182 0.099802289140 -1.823 0.068344 .
## stfdem10 -0.108168932476 0.114631143533 -0.944 0.345374
## gndr2 -0.095522183947 0.027188933002 -3.513 0.000444 ***
## agea 0.003944283840 0.001081100371 3.648 0.000265 ***
## rlgdgr1 0.052459426455 0.056206967531 0.933 0.350665
## rlgdgr2 0.022959018268 0.053383550864 0.430 0.667145
## rlgdgr3 0.125236929684 0.051573759421 2.428 0.015180 *
## rlgdgr4 0.091105132921 0.058134458505 1.567 0.117099
## rlgdgr5 0.000894788710 0.046968759233 0.019 0.984801
## rlgdgr6 0.059934454225 0.051558090456 1.162 0.245063
## rlgdgr7 -0.007731683715 0.051399015186 -0.150 0.880431
## rlgdgr8 0.007929514283 0.055342018474 0.143 0.886069
## rlgdgr9 -0.075097836124 0.085721803787 -0.876 0.381007
## rlgdgr10 0.175815400780 0.068045281012 2.584 0.009780 **
## yrpy -0.000000008538 0.000000007710 -1.107 0.268132
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 206.3327)
##
## Null deviance: 1622523 on 17028 degrees of freedom
## Residual deviance: 1532064 on 16960 degrees of freedom
## AIC: NA
##
## Number of Fisher Scoring iterations: 6
## Analysis of Deviance Table
##
## Model 1: nwspol ~ polintr + eisced + trstprl + eduyrs + netusoft + stfeco +
## stfgov + stfdem + gndr + agea + rlgdgr + yrpy
## Model 2: nwspol ~ polintr + eisced + trstprl + eduyrs + netusoft + stfeco +
## stfgov + stfdem + agea + rlgdgr + yrpy
## Resid. Df Resid. Dev Df Deviance F Pr(>F)
## 1 16960 1532064
## 2 16961 1534617 -1 -2552.4 12.37 0.0004373 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Yes, Gender plays a role for the quasi poisson model. This can be
assured with this test.
## Analysis of Deviance Table
##
## Model 1: nwspol ~ polintr + eisced + trstprl + eduyrs + netusoft + stfeco +
## stfgov + stfdem + gndr + agea + rlgdgr + yrpy
## Model 2: nwspol ~ polintr + eisced + trstprl + eduyrs + netusoft + stfeco +
## stfgov + gndr + agea + rlgdgr + yrpy
## Resid. Df Resid. Dev Df Deviance F Pr(>F)
## 1 16960 1532064
## 2 16970 1534358 -10 -2293.3 1.1114 0.3488
To compare it with the variable of “stfdem” about how satisfied the
participants of the survey are about how the democracy in their country
works. This variable doesn’t play a role to predict the media
consumption according to the quasipoisson model.
The results can be concluded that according to the models there is
some evidence, that the factors Interest in politics, age, and gender
are influencing the media consumption.
3.3 GLM Binomial
For the binary data we are using the following question from the
survey: There are different ways of trying to improve things in
[country] or help prevent things from going wrong. During the last 12
months, have you done any of the following? Have you... ...posted or
shared anything about politics online, for example on blogs, via email
or on social media such as Facebook or Twitter?
Graphical Analysis

Fitting the binary model (logistic regression)
If someone posts online is dependent on the age of the person. Older
people are not that tech-savy and therefore, have a higher inhibition to
post online. On the other hand, young people grew up with social media
and therefore are more likely to post political induced things.
##
## Call:
## glm(formula = postonline ~ age.na, family = "binomial", data = ess9_binary.na)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9792 -0.7141 -0.5696 -0.4445 2.1626
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.069127 0.140640 -0.492 0.623
## age.na -0.027793 0.002954 -9.408 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2232.0 on 2211 degrees of freedom
## Residual deviance: 2138.1 on 2210 degrees of freedom
## AIC: 2142.1
##
## Number of Fisher Scoring iterations: 4
##
## Call:
## glm(formula = postonline ~ age.na + eduyrs.na + interest.fac +
## boycott.fac + vote.fac, family = "binomial", data = ess9_binary.na)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.4233 -0.7072 -0.5132 -0.2928 2.5577
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.095283 0.363131 0.262 0.793018
## age.na -0.038720 0.003683 -10.513 < 0.0000000000000002 ***
## eduyrs.na 0.034592 0.017497 1.977 0.048043 *
## interest.fac.L 1.135895 0.293125 3.875 0.000107 ***
## interest.fac.Q 0.195537 0.222651 0.878 0.379824
## interest.fac.C 0.016625 0.133436 0.125 0.900846
## boycott.fac2 -0.674136 0.116343 -5.794 0.00000000686 ***
## vote.facNo -0.064151 0.206937 -0.310 0.756560
## vote.facNot eligible -0.018313 0.201498 -0.091 0.927585
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2232.0 on 2211 degrees of freedom
## Residual deviance: 2006.8 on 2203 degrees of freedom
## AIC: 2024.8
##
## Number of Fisher Scoring iterations: 5
## (Intercept) age.na eduyrs.na
## 1.0999705 0.9620199 1.0351970
## interest.fac.L interest.fac.Q interest.fac.C
## 3.1139580 1.2159638 1.0167642
## boycott.fac2 vote.facNo vote.facNot eligible
## 0.5095967 0.9378635 0.9818538
Interpretation: By increasing the age by one
year, the risk in odds will be increasing by approx. 1 time to post
something political online.
The odds for posting online by having a low interest in politics is
about 3.1 times higher than for persons that have no interest at
all.
3.5 Neural Network
Additional to “classic” linear models and GLM options, there are
neural networks for analyzing and predicting data.
Within this chapter two types of neural network model are applied to
two different questions.
- Predicting the values for the continuous variable
- Predicting the values for the categorical variable indicating the 5
levels of frequency of usage of internet
3.5.1 continious variable
## tibble [17,029 × 14] (S3: tbl_df/tbl/data.frame)
## $ nwspol : num [1:17029] 60 45 60 120 15 60 30 30 10 10 ...
## $ polintr : num [1:17029] 4 3 4 2 4 1 2 3 2 2 ...
## $ trstprl : num [1:17029] 6 0 0 6 4 3 3 7 7 5 ...
## $ eisced : num [1:17029] 2 3 3 3 3 4 3 6 2 7 ...
## $ eduyrs : num [1:17029] 12 11 12 12 13 21 18 17 9 17 ...
## $ stfeco : num [1:17029] 5 6 1 10 9 7 6 7 6 8 ...
## $ stfgov : num [1:17029] 6 8 3 10 8 2 7 2 7 6 ...
## $ stfdem : num [1:17029] 6 6 3 10 7 3 10 6 8 7 ...
## $ gndr : num [1:17029] 2 1 1 1 2 1 1 1 1 1 ...
## $ agea : num [1:17029] 40 63 56 48 41 27 49 42 50 35 ...
## $ rlgdgr : num [1:17029] 4 1 8 0 3 3 2 0 3 2 ...
## $ netusoft: num [1:17029] 4 5 1 1 4 5 5 5 5 5 ...
## $ psppsgva: num [1:17029] 2 2 2 5 1 3 1 1 2 3 ...
## $ yrpy : num [1:17029] 31200 30600 18000 31200 37200 18000 20400 17400 45600 70000 ...
Prepare for Training

Fit the Network
Predict the test set

And calculate the RMSE
## [1] 131.4847
Redo with caret and Cross Validation
```{#{r caret applied again, collapse=TRUE, message=FALSE,
warning=FALSE} #set.seed(42) #tuGrid <- expand.grid(.layer1=c(1:2),
.layer2=c(0,2), .layer3=c(0))
#trCtrl <- trainControl( # method = ‘repeatedcv’, #number = 4, #
repeats = 8, # returnResamp = ‘final’ #)
#models <- train( # x = ess9_ann %>% dplyr::select(-nwspol), #
y = ess9_ann_scaled %>% pull(nwspol), # method = ‘neuralnet’, metric
= ‘RMSE’, # linear.output = FALSE, # be careful, does only work on x!
#preProcess = c(‘center’, ‘scale’), #tuneGrid = tuGrid, #trControl =
trCtrl #)
<img src="ESS_DE_files/figure-html/unnamed-chunk-41-1.png" width="672" />
and extract the best model
### 3.5.2 Categorical variable
NN models can be used for categorical variables as well. In this chapter the goal is to find a classification of values to the categories. As variable the frequency of usage of the internet is used.
tibble [17,029 × 14] (S3: tbl_df/tbl/data.frame)
$ nwspol : num [1:17029] 60 45 60 120 15 60 30 30 10 10 …
$ polintr : num [1:17029] 4 3 4 2 4 1 2 3 2 2 …
$ trstprl : num [1:17029] 6 0 0 6 4 3 3 7 7 5 …
$ eisced : num [1:17029] 2 3 3 3 3 4 3 6 2 7 …
$ eduyrs : num [1:17029] 12 11 12 12 13 21 18 17 9 17 …
$ stfeco : num [1:17029] 5 6 1 10 9 7 6 7 6 8 …
$ stfgov : num [1:17029] 6 8 3 10 8 2 7 2 7 6 …
$ stfdem : num [1:17029] 6 6 3 10 7 3 10 6 8 7 …
$ gndr : num [1:17029] 2 1 1 1 2 1 1 1 1 1 …
$ agea : num [1:17029] 40 63 56 48 41 27 49 42 50 35 …
$ rlgdgr : num [1:17029] 4 1 8 0 3 3 2 0 3 2 …
$ netusoft: Factor w/ 5 levels “1”,“2”,“3”,“4”,..: 4 5 1 1 4 5 5 5 5
5 …
$ psppsgva: num [1:17029] 2 2 2 5 1 3 1 1 2 3 …
$ yrpy : num [1:17029] 31200 30600 18000 31200 37200 18000 20400
17400 45600 70000 …
#### Have a quick look at the Data
<img src="ESS_DE_files/figure-html/unnamed-chunk-45-1.png" width="672" />
<img src="ESS_DE_files/figure-html/unnamed-chunk-46-1.png" width="672" />
#### Prepare the Data for Training
The distribution of our different prediction classes in the train and test data sets can be compared. The data shows a concentration of 4 and 5 values. The participants of this survey are often and frequently using the internet.
train
netusoft FALSE TRUE
1 90 515
2 91 516
3 106 604
4 210 1193
5 2055 11649
#### Train the Neural Network
Call the `neuralnet` function creating a network with two hidden layer.
Plot the resulting network including the weights
#### Make Predictions
[,1] [,2] [,3] [,4] [,5]
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[1922,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1923,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1924,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1925,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854
[1926,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1927,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1928,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1929,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1930,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1931,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1932,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1933,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1934,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1935,] 0.005956734 0.02358905 0.03199785 0.06104834 0.87740525
[1936,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1937,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1938,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854
[1939,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1940,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1941,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1942,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1943,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1944,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1945,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854
[1946,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1947,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1948,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1949,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1950,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1951,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1952,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1953,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1954,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1955,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1956,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1957,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1958,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1959,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1960,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1961,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1962,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1963,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1964,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1965,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1966,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1967,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1968,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1969,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1970,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1971,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1972,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1973,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1974,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1975,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1976,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1977,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1978,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1979,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1980,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1981,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1982,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1983,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1984,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1985,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1986,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1987,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1988,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1989,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1990,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1991,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1992,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1993,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1994,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1995,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1996,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1997,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1998,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[1999,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2000,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2001,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2002,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2003,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2004,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2005,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2006,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2007,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2008,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2009,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2010,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2011,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2012,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2013,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2014,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2015,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2016,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2017,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2018,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2019,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2020,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2021,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2022,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2023,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2024,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2025,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2026,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2027,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2028,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2029,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2030,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2031,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2032,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2033,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2034,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2035,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2036,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2037,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2038,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2039,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2040,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2041,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2042,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2043,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2044,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2045,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2046,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2047,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2048,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2049,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2050,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2051,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2052,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2053,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2054,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2055,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2056,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2057,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2058,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2059,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2060,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2061,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2062,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2063,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2064,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2065,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2066,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2067,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2068,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2069,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2070,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2071,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2072,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2073,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2074,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2075,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2076,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2077,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2078,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2079,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2080,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2081,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2082,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2083,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2084,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2085,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2086,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2087,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2088,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2089,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2090,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2091,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2092,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2093,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2094,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2095,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2096,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2097,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2098,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2099,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2100,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2101,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2102,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2103,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2104,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2105,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2106,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2107,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2108,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2109,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2110,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2111,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2112,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2113,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2114,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2115,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2116,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2117,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2118,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2119,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2120,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2121,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2122,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2123,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2124,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2125,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2126,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2127,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2128,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2129,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2130,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2131,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2132,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2133,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2134,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2135,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2136,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2137,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2138,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2139,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2140,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2141,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2142,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2143,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2144,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2145,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2146,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2147,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2148,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2149,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2150,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2151,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2152,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2153,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2154,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2155,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
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[2388,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2389,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2390,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2391,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2392,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2393,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2394,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2395,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2396,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2397,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2398,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2399,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2400,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2401,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2402,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2403,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2404,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2405,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2406,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2407,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2408,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2409,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2410,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2411,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2412,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2413,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2414,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2415,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2416,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2417,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2418,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2419,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2420,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2421,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2422,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2423,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2424,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2425,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2426,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2427,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2428,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2429,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2430,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854
[2431,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2432,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2433,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2434,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2435,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2436,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2437,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2438,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2439,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2440,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2441,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2442,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2443,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2444,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2445,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2446,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2447,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2448,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2449,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2450,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2451,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2452,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2453,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2454,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2455,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2456,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2457,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2458,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2459,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2460,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2461,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2462,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2463,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2464,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2465,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2466,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2467,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2468,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2469,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2470,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2471,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2472,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2473,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2474,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2475,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2476,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2477,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2478,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2479,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2480,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2481,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2482,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2483,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2484,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2485,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2486,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2487,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2488,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2489,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2490,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2491,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2492,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2493,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2494,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2495,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2496,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2497,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2498,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2499,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2500,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2501,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2502,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2503,] 0.198939981 0.10213039 0.09535854 0.20021931 0.40336854
[2504,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2505,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2506,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2507,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2508,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2509,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2510,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2511,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2512,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2513,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2514,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2515,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2516,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2517,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2518,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2519,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2520,] 0.005956734 0.02358905 0.03199785 0.06104834 0.87740525
[2521,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2522,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2523,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2524,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2525,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2526,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2527,] 0.005956734 0.02358905 0.03199785 0.06104834 0.87740525
[2528,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2529,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2530,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2531,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2532,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2533,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2534,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2535,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2536,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2537,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2538,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2539,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2540,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2541,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2542,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2543,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2544,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2545,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2546,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2547,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2548,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2549,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2550,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2551,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
[2552,] 0.034583946 0.03523991 0.04139680 0.08169301 0.80708646
Find class (i.e. output neuron) with the highest probability and convert this back into a factor
[1] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5
[38] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5
[75] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5
[112] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[149] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[186] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[223] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[260] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[297] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[334] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[371] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[408] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[445] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[482] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[519] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[556] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[593] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[630] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[667] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[704] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[741] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[778] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[815] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[852] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[889] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[926] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[963] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1000] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1037] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1074] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1111] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1148] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1185] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1222] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1259] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1296] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1333] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1370] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1407] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1444] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1481] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1518] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1555] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1592] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1629] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1666] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1703] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1740] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1777] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1814] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1851] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1888] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1925] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1962] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[1999] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2036] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2073] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2110] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2147] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2184] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2221] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2258] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2295] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 5 5 5 5 5
5 5 5 5 5 5
[2332] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2369] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2406] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2443] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2480] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5
[2517] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5
Levels: 1 2 3 4 5
#### Evaluate the Results
The confusion maztrix shows
Confusion Matrix and Statistics
Reference
Prediction 1 2 3 4 5
1 1 0 0 0 89
2 0 0 0 0 91
3 0 0 0 0 106
4 0 0 0 0 210
5 0 0 0 0 2055
Overall Statistics
Accuracy : 0.8056
95% CI : (0.7897, 0.8208)
No Information Rate : 0.9996
P-Value [Acc > NIR] : 1
Kappa : 0.0036
Mcnemar’s Test P-Value : NA
Statistics by Class:
Class: 1 Class: 2 Class: 3 Class: 4 Class: 5
Sensitivity 1.0000000 NA NA NA 0.805566
Specificity 0.9651117 0.96434 0.95846 0.91771 1.000000
Pos Pred Value 0.0111111 NA NA NA 1.000000
Neg Pred Value 1.0000000 NA NA NA 0.002012
Prevalence 0.0003918 0.00000 0.00000 0.00000 0.999608
Detection Rate 0.0003918 0.00000 0.00000 0.00000 0.805251
Detection Prevalence 0.0352665 0.03566 0.04154 0.08229 0.805251
Balanced Accuracy 0.9825559 NA NA NA 0.902783
#### Optimize Network Structure
First we need to remodel the data due to some limitations of `caret`
netusoft netusoft2 netusoft3 netusoft4 netusoft5
1 1 0 0 1 0
2 1 0 0 0 1
3 1 0 0 0 0
4 1 0 0 0 0
5 1 0 0 1 0
6 1 0 0 0 1
And have a look at the different models
<img src="ESS_DE_files/figure-html/unnamed-chunk-55-1.png" width="672" />
And try out the best model
The error for both types of neutral network model is still high, the optimization options were limited, as changing variables lead to high computing times. Nevertheless the models predict values for the two chosen variables. The continuous model lead to better results, comparing the calculated errors.
## 3.6 Support Vector Machine
The goal in this chapter is to classify people on their political scale. Leftist on the left, center on the center and right-wing people on the right. The response variable *scale_cat* is in the survey categorized from 0 = left to 10 = right. For this model to work the variable was further categorized to left, center and right. \
The objective is to see if we can classify the persons on their political scale according to socio-demographic predictor variable.
left center right NA’s
987 1149 125 97
0 1 2 3 4 5 6 7 8 9 10 NA’s
95 64 186 340 302 826 198 125 86 14 25 97
[1] “integer”
left center right NA’s
tibble [1,089 × 7] (S3: tbl_df/tbl/data.frame)
$ age.na : num [1:1089] 26 54 41 47 48 60 44 51 26 79 …
$ interest.fac: Ord.factor w/ 4 levels “none at all”<..: 2 2 2 3
4 4 3 3 2 3 …
$ scale_cat : Factor w/ 3 levels “left”,“center”,..: 2 1 1 1 2 1 2 2
2 3 …
$ eduyrs.na : num [1:1089] 13 14 14 13 18 16 0 14 10 7 …
$ sat.dem.fac : Factor w/ 11 levels “0”,“1”,“2”,“3”,..: 8 6 8 6 10 9
6 6 5 5 …
$ yearpay : num [1:1089] 288000 72000 19200 26400 72000 …
$ vote.fac : Factor w/ 3 levels “Yes”,“No”,“Not eligible”: 2 1 1 1 1
1 2 1 1 1 …
### Have a quick look at the Data
<img src="ESS_DE_files/figure-html/unnamed-chunk-59-1.png" width="672" />
It is not possible to see a clear classifcation of groups by this plot.
<img src="ESS_DE_files/figure-html/unnamed-chunk-60-1.png" width="672" />
There can bee seen a small grouping on the left side of the plot (young people and middle education level).
### Prepare the Data for Training
### Create some easy Variables to access Data
### Train the Neural Network
Call:
svm(formula = scale_cat ~ ., data = train, kernel = “linear”, cost =
10,
scale = TRUE)
Parameters:
SVM-Type: C-classification
SVM-Kernel: linear
cost: 10
Number of Support Vectors: 833
( 385 408 40 )
Number of Classes: 3
Levels:
left center right
<img src="ESS_DE_files/figure-html/unnamed-chunk-64-1.png" width="672" />
The best cost parameter is 0.1.
<img src="ESS_DE_files/figure-html/unnamed-chunk-67-1.png" width="672" />
<img src="ESS_DE_files/figure-html/unnamed-chunk-68-1.png" width="672" />
The plots suggest, that linear may not be the right approach to get a classification right.
### Make Predictions
### Evaluate the Results
Confusion Matrix and Statistics
Reference
Prediction left center right
left 30 25 0
center 42 59 7
right 0 0 0
Overall Statistics
Accuracy : 0.546
95% CI : (0.4663, 0.624)
No Information Rate : 0.5153
P-Value [Acc > NIR] : 0.2405
Kappa : 0.109
Mcnemar’s Test P-Value : NA
Statistics by Class:
Class: left Class: center Class: right
Sensitivity 0.4167 0.7024 0.00000
Specificity 0.7253 0.3797 1.00000
Pos Pred Value 0.5455 0.5463 NaN
Neg Pred Value 0.6111 0.5455 0.95706
Prevalence 0.4417 0.5153 0.04294
Detection Rate 0.1840 0.3620 0.00000
Detection Prevalence 0.3374 0.6626 0.00000
Balanced Accuracy 0.5710 0.5411 0.50000
[**Interpretation**]{.underline}: the accuracy of the linear model is at a bit over 50%. It makes sense, as the descriptive plots hinted that there cannot be a straight "division" line.
### Try again with other parameters
Call:
svm(formula = scale_cat ~ ., data = train, kernel = “radial”, cost =
100000,
scale = TRUE)
Parameters:
SVM-Type: C-classification
SVM-Kernel: radial
cost: 100000
Number of Support Vectors: 661
( 300 322 39 )
Number of Classes: 3
Levels:
left center right
<img src="ESS_DE_files/figure-html/unnamed-chunk-72-1.png" width="672" />
Call:
best.tune(METHOD = svm, train.x = scale_cat ~ ., data =
d.ess9_supportvec,
ranges = list(cost = c(0.001, 0.01, 0.1, 1, 5, 10, 100, 1000)),
kernel = “radial”, gamma = c(0.5, 1, 2, 3, 4))
Parameters:
SVM-Type: C-classification
SVM-Kernel: radial
cost: 1
Number of Support Vectors: 1016
<img src="ESS_DE_files/figure-html/unnamed-chunk-75-1.png" width="672" />
test_pred1
left center right
Confusion Matrix and Statistics
Reference
Prediction left center right
left 33 27 2
center 39 56 5
right 0 1 0
Overall Statistics
Accuracy : 0.546
95% CI : (0.4663, 0.624)
No Information Rate : 0.5153
P-Value [Acc > NIR] : 0.24051
Kappa : 0.1194
Mcnemar’s Test P-Value : 0.07689
Statistics by Class:
Class: left Class: center Class: right
Sensitivity 0.4583 0.6667 0.000000
Specificity 0.6813 0.4430 0.993590
Pos Pred Value 0.5323 0.5600 0.000000
Neg Pred Value 0.6139 0.5556 0.956790
Prevalence 0.4417 0.5153 0.042945
Detection Rate 0.2025 0.3436 0.000000
Detection Prevalence 0.3804 0.6135 0.006135
Balanced Accuracy 0.5698 0.5549 0.496795
[**Interpretation**]{.underline}: the accuracy of the linear model is at a bit over 50%. It has improved when compared to the linear classification approach but it is still unsatisfactory.
#### Tune costing
<img src="ESS_DE_files/figure-html/unnamed-chunk-79-1.png" width="672" />
With alsmost every additional cost the accuracy of the model increases. However, it stagnates with cost = 2. A small c indicates that the penalization for misclassification is small and therefore, it represents a soft margin. Inside the margins, the sample that is located there will not be penalized much.
[1] center center center center center left left left center
left
[11] center left left left center center left center left
center
[21] center center center center left center center left left
center
[31] left center center left center center center left left
left
[41] left center center left center left left center center
center
[51] center center center left center left left center left
center
[61] center left center center left center center left center
left
[71] center center center left left center center center left
center
[81] left center center center center left center center left
center
[91] left center center center center center left center center
left
[101] left center center left left left center center center
center
[111] left center center left center center center center center
center
[121] center left center left center center center center center
left
[131] left left center left left left center left center center
[141] left center left left left center center center center
center
[151] left center left left center center center left center
center
[161] left left center left left center center left left left
[171] center center center center center left left left center
center
[181] center center center center left center center center center
center
[191] left center center left center center center left center
center
[201] center center center left left center center left left
center
[211] center center center left center center left center left
center
[221] center center center center center center center center center
center
[231] left left center center left center center center center
center
[241] center left center center left center left center center
left
[251] center center center center left left left center center
center
[261] center center center center center left center center left
left
[271] left center left center left center left left center
center
[281] left center center left left left center center left
center
[291] left left center left center center center center center
center
[301] center center left left center center center center left
center
[311] center center center center left left center center left
center
[321] center center left left left center
Levels: left center right
Confusion Matrix and Statistics
test_pred_grid left center right
left 74 40 3
center 70 128 11
right 0 0 0
Overall Statistics
Accuracy : 0.6196
95% CI : (0.5645, 0.6726)
No Information Rate : 0.5153
P-Value [Acc > NIR] : 0.00009487
Kappa : 0.2558
Mcnemar’s Test P-Value : 0.00005979
Statistics by Class:
Class: left Class: center Class: right
Sensitivity 0.5139 0.7619 0.00000
Specificity 0.7637 0.4873 1.00000
Pos Pred Value 0.6325 0.6124 NaN
Neg Pred Value 0.6651 0.6581 0.95706
Prevalence 0.4417 0.5153 0.04294
Detection Rate 0.2270 0.3926 0.00000
Detection Prevalence 0.3589 0.6411 0.00000
Balanced Accuracy 0.6388 0.6246 0.50000
```
Interpretation: The classification of the political
affiliation can surpass the 50% accuracy mark but much more is not
achievable. This model is not made for the kernel = linear but rather
kernel = radial. It is a much more complex data and it needs to be
treated that way.